What Is 2/3 - 2/9? Find The Simplest Form!
Table of Contents :
To solve the problem of ( \frac{2}{3} - \frac{2}{9} ) and find its simplest form, we will go through a series of steps. This process involves finding a common denominator, performing the subtraction, and simplifying the result if possible. Let’s break it down step by step!
Understanding Fractions
Fractions are a way to represent parts of a whole. The top number (numerator) indicates how many parts we have, while the bottom number (denominator) shows how many equal parts the whole is divided into. To perform operations with fractions, especially subtraction, we often need to find a common denominator.
Step 1: Identify the Denominators
In our case, we have two fractions:
- ( \frac{2}{3} ) (with a denominator of 3)
- ( \frac{2}{9} ) (with a denominator of 9)
Step 2: Find the Least Common Denominator (LCD)
The least common denominator (LCD) is the smallest number that both denominators can divide into without leaving a remainder. Here are the multiples of the denominators:
- Multiples of 3: 3, 6, 9, 12, 15...
- Multiples of 9: 9, 18, 27...
The smallest common multiple is 9. Therefore, the least common denominator for ( \frac{2}{3} ) and ( \frac{2}{9} ) is 9.
Step 3: Convert to Equivalent Fractions
Next, we will convert ( \frac{2}{3} ) to an equivalent fraction with a denominator of 9.
To convert ( \frac{2}{3} ):
- Multiply both the numerator and denominator by 3 (because ( 3 \times 3 = 9 )): [ \frac{2 \times 3}{3 \times 3} = \frac{6}{9} ]
Now, we have:
- ( \frac{2}{3} = \frac{6}{9} )
- ( \frac{2}{9} ) stays the same.
Step 4: Subtract the Fractions
Now that both fractions have the same denominator, we can easily perform the subtraction:
[ \frac{6}{9} - \frac{2}{9} = \frac{6 - 2}{9} = \frac{4}{9} ]
Step 5: Simplify if Necessary
Now, we will check if ( \frac{4}{9} ) can be simplified further.
- The numerator is 4 and the denominator is 9.
- The greatest common divisor (GCD) of 4 and 9 is 1, which means that ( \frac{4}{9} ) is already in its simplest form.
Final Result
The simplest form of ( \frac{2}{3} - \frac{2}{9} ) is:
[ \boxed{\frac{4}{9}} ]
Key Takeaways
- To subtract fractions, always find a common denominator.
- Convert fractions to equivalent fractions with the same denominator before performing the operation.
- After completing the operation, check if the result can be simplified further.
In conclusion, understanding how to work with fractions is essential for solving various mathematical problems. The process of finding a common denominator and simplifying results is a foundational skill in arithmetic. Whether you're dealing with simple numbers or complex equations, these basic principles remain the same.